HSA.CED.A.2 Math Practice Questions

Practice playeasy

In $y = 3x + 1$ , what is the slope?

In slope-intercept form $y = mx + b$ , the coefficient of $x$ is the slope. Here $m = 3$ .

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A line passes through the points $(0, -3)$ and $(4, 1)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{1 - (-3)}{4 - 0} = 1$ . Because the line passes through $(0, -3)$ , the $y$ -intercept is $b = -3$ where $x = 0$ . The equation is $y = x - 3$ .

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Which value of $k$ makes $x^{2}+2x+k=0$ have solutions $x=-6$ and $x=4$ ?

If the zeros are $x=-6$ and $x=4$ , that means the factors of the equation are $(x+6)$ and $(x-4)$ . The product of these factors is $x^{2}+2x-24$ . Comparing with $x^{2}+2x+k$ , the missing constant is $k=-24$ .

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A moving crew packs small boxes that weigh $12$ pounds each and large boxes that weigh $35$ pounds each. The crew packs $x$ small boxes and $y$ large boxes with a combined weight of $470$ pounds. Which equation represents this situation?

The small boxes weigh $12x$ pounds in all and the large boxes weigh $35y$ pounds in all. The combined weight is $470$ pounds, so $12x + 35y = 470$ .

Practice playeasy

In $y = -2x + 7$ , what is the $y$ -intercept?

In slope-intercept form $y = mx + b$ , the constant term $b$ is the $y$ -intercept. Here $b = 7$ .

Practice playmedium

A line passes through the points $(1, -4)$ and $(5, 4)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{4 - (-4)}{5 - 1} = 2$ . Substitute $(1, -4)$ : $-4 = 2(1) + b$ , so $b = -6$ . The equation is $y = 2x - 6$ .

Practice playeasy

For which value of $n$ does $x^{2}-7x+n=0$ have solutions $x=1$ and $x=6$ ?

If the zeros are $x=1$ and $x=6$ , that means the factors of the equation are $(x-1)$ and $(x-6)$ . The product of these factors is $x^{2}-7x+6$ . Comparing with $x^{2}-7x+n$ , the missing constant is $n=6$ .

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A community garden has plots for tomato plants that each use $4.5$ square meters and plots for herb plants that each use $1.5$ square meters. The garden uses a total of $36$ square meters for $x$ tomato plots and $y$ herb plots. Which equation represents this situation?

The tomato plots use $4.5x$ square meters and the herb plots use $1.5y$ square meters. The total area used is $36$ square meters, so $4.5x + 1.5y = 36$ .

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Skills aligned to HSA.CED.A.2

Linear equation forms

Linear equation from two points (SAT)

Quadratic missing coefficient from roots (ACT)

Writing a two-variable equation from context

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